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Looking for Those Natural Numbers: Dimensionless Constants and the Idea of Natural Measurement1

Published online by Cambridge University Press:  26 September 2008

Philip Mirowski
Affiliation:
Department of Economics and Reilly Center for the History and Philosophy of Science University of Notre Dame

Abstract

Many find it “notoriously difficult to see how societal context can affect in any essential way how someone solves a mathematical problem or makes a measurement.” That may be because it has been a habit of western scientists to assert their numerical schemes were untainted by any hint of anthropomorphism. Nevertheless, that Platonist penchant has always encountered obstacles in practice, primarily because the stability of any applied numerical scheme requires some alien or external warrant.

This paper surveys the history of measurement standards, physical dimensions and dimensionless constants as one instance of the quest to purge all anthropomorphic taint first in the metric system, then in the dimensions provided by the atom, then in physical constants intelligible to extraterrestrials, only then to end up back at overt anthropomorphism in the late 20th century. This suggests that the “naturalness” of natural numbers has always been conceptualized in locally contingent cultural terms.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1992

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Footnotes

1

This paper was inspired by some remarks by Martin Klein during his lectures at Yale on the history of early twentieth-century physics; but he cannot be held responsible for my interpretations. I also thank Ted Porter for his help with the philosophical issues.

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